Answer:
0.78 m
Explanation:
By the conservation of energy, the energy that they gain from potential energy, must be equal to the kinetic energy. So, for Adolf:
Ep = Ek
ma*g*ha = ma*va²/2
Where ma is the mass of Adolf, g is the gravity acceleration (10 m/s²), ha is the height that he reached, and va is the velocity. So:
100*10*0.51 = 100*va²/2
50va² = 510
va² = 10.2
va = √10.2
va = 3.20 m/s
Before the push, both of them are in rest, so the momentum must be 0. The system is conservative, so the momentum after the push must be equal to the momentum before the push:
ma*va + me*ve = 0, where me and ve are the mass and velocity of Ed. So:
100*3.20 + 81ve = 0
81ve = 320
ve = 3.95 m/s
By the conservation of energy for Ed:
me*g*he = me*ve²/2
81*10*he = 81*(3.95)²/2
810he = 631.90
he = 0.78 m
